Learning Resources
Lesson
Before beginning this lesson, recall all the characteristics of functions that you have previously encountered and make a list in your notebook such that you can use these as a basis for a discussion of the concept of function with your teacher and classmates. Be specific and write in your own words (your teacher may request a copy of your notes).
After completing your list, click here to find information regarding functions.
Focus A
Complete the focus questions under the Activities section of this lesson.
In completing the Focus Questions, read the descriptions given and sketch a graph to represent each in your notebook. After you have completed the graphs, compare yours to those in the textbook to decide on the proper match. Discuss your results with others in the class and your on-line teacher. ( Not every graph in the text is used in the matching process)
Continue on to Investigation 1 if you have the focus completed and discussed.
Investigation 1
Before beginning this investigation consider the following dilemma:
If you were given the opportunity, would you rather receive $1 000 000 or for a month of 31 days would you rather receive 1 cent the first day, 2 cents the second day, 4 cents the third day, 8 cents the fourth day and so on?
Think about this problem and decide on what you would do and why?
After you have contemplated the above situation read the introduction to this investigation. You can read extra information on the topic of nuclear fission by visiting the web addresses given in the sidebar of you textbook.
Note the stages of the process where the neutron hits the nucleus and produces more neutrons by hitting Go forward one frame button below (look for a pattern):
In this investigation, you will explore the common properties of geometric sequences, including the calculation of a common ratio. From this the growth will be exponential.
Step A : Note the definition of sequence in your textbook and recall its use from Unit 1. Make sure you list as many patterns as you can find regarding this sequence.
For Step B, you should discover an interesting fact concerning the ratio of consecutive terms in a geometric sequence.
The procedures for Steps A and B are repeated in Steps B and D. In these steps, the original sequence is changed by multiplying by a constant. Again note the interesting result concerning the ratios of consecutive terms.
The Think About (p.111) should be completed with this investigation. Using the sequences of differences for Steps A, C and D, determine if the sequences are arithmetic, quadratic or cubic. Why? or Why not? How can we describe the sequence?
Before beginning the Activities Section, click here for a discussion of the problem above.
Activity
Focus Questions p.108 - p.109. Complete 1 and 2
Investigation Questions p.111. Complete 3, 4, 5 and 6
Think About p.111 (2 items)
Check Your Understanding p.112 - p.114. Complete 7 to 14 inclusive
When you have completed these questions, ask your on-site teacher to get the solutions for you from the Teacher's Resource Binder and check them against your answers. After you do this, if there is something you had trouble with and still do not understand, contact your on-line teacher for help.
After you do the assigned activities, continue on to the Test Yourself section below for a quick quiz on this lesson.
Test Yourself
- Write the sequence 4, 12, 36, 108, ...as a power or a multiple of a power.
- A picture that is 12 by 15 is to be reduced on a photocopy machine.. If each reductions is 20% of the original, how many times must it be reduced to obtain a picture that is approximately 5 by 6?
Click here for suggested solutions.